I think my kitten is sick, what could be wrong?

If you don't take her to the vet, you won't know. Bleeding from the nose could be trauma or injury to the sinus membranes, sinus bones or to who-knows-what? Only the vet could tell with an exam and possibly an X-ray. Otherwise, you are just taking a chance that she may or may not be O.K. She is quite small and it doesn't take a lot of time for a small kitten to go downhill. She should also be bottle fed at that young age. This is very important to her well-being, but her immediate health is most important.